Receiver architecture for linear modulation based communication systems

ABSTRACT

A receiver for Filter Bank Multicarrier frequency spread signals such as FBMC, FBMC/OQAM, OFDM, comprises a linear phase rotation module adapted to introduce a linear phase rotation to a received time domain signal, a discrete Fourier transform and a Finite Impulse response digital filter. The coefficients of the digital filter define a shift of the frequency response of the prototype filter of the receiver, and the coefficients of the digital filter are fixed so as to compensate the linear phase rotation introduced by the filter. The frequency shift introduced may be equal to the reciprocal of a power of two of the modulation sub carrier spacing.

FIELD OF THE INVENTION

The present invention relates to receiver architectures for linearmodulation based communication systems, and their design.

BACKGROUND OF THE INVENTION

Forthcoming mobile communication systems will be expected to provideubiquitous connectivity and seamless service delivery in allcircumstances. The large number of devices and the coexistence ofhuman-centric and machine type applications expected will lead to alarge diversity of communication scenarios and characteristics. In thiscontext, many advanced communication techniques are under investigation.Each of these techniques is typically optimised for a subset of theforeseen communication scenarios.

One category of techniques is based on filter-bank multicarriercommunications principles. A filter-bank multicarrier (FBMC)communications system is composed of a synthesis filter for modulationand an analysis filter for demodulation. The synthesis and analysisfilters are composed of M channels, denoted by sub-carriers for acommunications system. The channel number m of the synthesis filtermodulates a complex signal c_(n)(m) carrying information at time samplen of the signal before up-sampling by N. This reflects the fact that thesignal is sampled in the synthesis filter, before the up-samplingoperation, and n correspond to a generic index of this signal. The datais then up-sampled by N, so (N−1) zeros are introduced between twoconsecutives n values. Each channel consists of an oversamplingoperation by N followed by a finite impulse response filter F_(m)(z).These operations can be expressed as follows:

Up-Sampling by N

$\begin{matrix}{{C_{{\uparrow N},k}(m)} = \left\{ \begin{matrix}{{{C_{\frac{k}{N}}(m)}{if}\mspace{14mu} {{mod}_{N}({kN})}} = 0} \\0\end{matrix} \right.} & (1)\end{matrix}$

$\begin{matrix}{{s_{m}(k)} = {\sum\limits_{l = {- \infty}}^{+ \infty}{{C_{{\uparrow N},{k - l}}(m)}{f_{m}(l)}}}} & (2) \\{{f_{m}(l)} = {{g(l)}e^{\frac{i\; 2\; \pi \; {lm}}{M}}}} & (3)\end{matrix}$

Filter by F_(m)(z)

g is referred to as the prototype filter, and is a function with afinite length L:g(k)=0 if k∉

0,L−1

.

The modulated signal s(k) at the output of the synthesis filter isobtained after the sum of each channel output:

$\begin{matrix}{{s(k)} = {\sum\limits_{m = 0}^{M - 1}{s_{m}(k)}}} & (4)\end{matrix}$

An equivalent relation between the input and output signal of thesynthesis filter can be expressed as follows:

$\begin{matrix}{{s(k)} = {\sum\limits_{m = 0}^{M - 1}{\sum\limits_{n = {- \infty}}^{+ \infty}{{c_{n}(m)}{g\left( {k - {nN}} \right)}e^{\frac{i\; 2\pi \; {km}}{M}}}}}} & (5)\end{matrix}$

This expression leads to the polyphase network representation of thesynthesis filter, which is computationally complex to implement whencompared to a direct synthesis filter representation.

As regards the analysis filter, the corresponding operations of thetransmitter for the M channels are comprised of the following operation:

Filtering by Hm(z):

$\begin{matrix}{{{r_{m}(k)} = {\sum\limits_{l = {- \infty}}^{+ \infty}{{r\left( {k - 1} \right)}{h_{m}(l)}}}},{{h_{m}(l)} = {{g(l)}e^{\frac{{- i}\; 2\pi \; {lm}}{M}}}}} & (6)\end{matrix}$

Down-Sampling by N:

d _(n)(m)=r _(m)(nN)  (7)

The equivalent relation between the input and output signals of theanalysis filter can be expressed as follows:

$\begin{matrix}{{d_{n}(m)} = {\sum\limits_{k = {- \infty}}^{+ \infty}{{s(k)}{g\left( {k - {nN}} \right)}e^{\frac{{- i}\; 2\pi \; {km}}{M}}}}} & (8)\end{matrix}$

This basic approach is used in numerous modulation schemes, and as suchthe design of filters implementing the described approach is animportant activity.

This definition of the FBMC technique corresponds to numerous modulationschemes depending on the design of the prototype filters and the choiceof the different set of parameters (M, N, L, . . . ). In other words,the technique described generates multiple carriers (as suggested by theMC part of the designation) and the choice of modulation scheme of eachcarrier may be defined separately, the choice of OQAM being one which isadvantageous for certain communications systems. One such modulationscheme is Filter-Bank Multi-Carrier with Offset Quadrature AmplitudeModulation (FBMC/OQAM) which is considered as a key enabler for thefuture flexible 5G air interface for example. It exhibits a spectrumshape with less out of band energy components compared to thetraditional Orthogonal Frequency-Division Multiplexing (OFDM) andenables better spectrum usage and improved mobility support. This ispossible thanks to the use of a prototype filter which makes it possibleto improve the time and frequency localization properties of thetransceiver. Orthogonality is preserved in the real field with the OQAMscheme. FBMC/OQAM implementation is similar to that of OFDM in that itit relies on Fast Fourier Transform (FFT) processing with an additionallow-complexity PolyPhase Network (PPN) filtering stage. However, thechoice of the prototype filter is crucial for FBMC/OQAM modulation, asthe time/frequency localization of this filter can significantly impactthe different performance levels and the frame structure of thecommunication system. Furthermore, the length of the prototype filterimpacts the receiver complexity considerably. Thus, design of newfilters is of high interest to improve robustness of FBMC/OQAM againstchannel impairments and to support the constraints imposed by various 5Gscenarios while preserving reasonable receiver complexity.

FBMC is a multicarrier transmission scheme that introduces a filter-bankto enable efficient pulse shaping for the signal conveyed on eachindividual subcarrier. This additional element represents an array ofband-pass filters that separate the input signal into multiplecomponents or subcarriers, each one carrying a single frequency sub-bandof the original signal. The process of decomposition performed by thefilter bank is called analysis (meaning analysis of the signal in termsof its components in each sub-band); the output of analysis is referredto as a sub-band signal with as many sub-bands as there are filters inthe filter bank. The reconstruction process is called synthesis,indicating reconstitution of a complete signal resulting from thefiltering process. Such a transceiver structure usually requires ahigher implementation complexity due not only to the filtering steps butalso to the modifications applied to the modulator/demodulatorarchitecture. However, the use of digital polyphase filter bankstructures together with the rapid growth of digital processingcapabilities in recent years have made FBMC a practically feasibleapproach. As a promising variant of filtered modulation schemes,FBMC/OQAM, (also sometimes referred to as OFDM/OQAM or staggeredmodulated multitone—SMT), can usually achieve a higher spectralefficiency than OFDM since it does not require the insertion of aCyclic-Prefix (CP). Additional advantages include the robustness againsthighly variant fading channel conditions and imperfect synchronizationsby selecting the appropriate prototype filter type and coefficients.4G/LTE is based on OFDM multicarrier modulation. In accordance with theBalian-Low theorem, OFDM:

1) respects the complex orthogonality,2) is poorly localized in frequency domain by adopting a rectangularwaveform,3) wastes part of the available bandwidth due to the addition of a CP.

Property 2 results in high Out-Of-Band Power Leakage (OOBPL), and largeguard-bands have to be inserted to respect Adjacent Channel LeakagePower Ratio (ACLR) requirements. Furthermore, it results in a poorrobustness against Doppler shift and spread. Further possibledisadvantages of the corresponding OFDM system are related to flexiblespectrum usage scenarios, where spectrum sharing and fragmented usageare not efficiently supported.

To overcome shortcomings 2) and 3) of OFDM, FBMC/OQAM:

a) relaxes to real field orthogonality,b) is better localized in time and frequency, depending on the usedprototype filter,c) uses available bandwidth efficiently to achieve a higher spectralefficiency.

Property a) is obtained by changing the way QAM symbols are mapped ontoeach subcarrier. Instead of sending a complex symbol (I and Q) ofduration T as in classical CP-OFDM, the real and imaginary parts areseparated and sent with an offset of T/2 (hence the name Offset-QAM).

Improvement b) comes from the introduction of the filter-bank andtherefore depends on its type and coefficients.

Property c) is the consequence of the absence of a CP. Previouspublished works have identified two major design criteria for anFBMC/OQAM system:

-   -   Time Frequency Localization (TFL) criterion: for a waveform that        is better localized in the time and frequency domains thanks to        the prototype filter. It is predictable that FBMC systems        exhibit better robustness than CP-OFDM in doubly-dispersive        channels and in the case of communications with synchronization        errors. To this end filter designs with the optimized TFL        criterion have been proposed, such as “Isotropic Orthogonal        Transform Algorithm with overlapping factor (OF) equals to 4”.    -   Lower sideband criterion: achieving low out-of-band power        leakage in frequency domain and for improving spectrum        coexistence with other systems. To this end, particular filter        types may be used such as “Martin-Mirabassi-Bellange with OF        equals to 4”, as considered for FBMC/OQAM during the PHYDYAS        project.

FBMC/OQAM System Description

FIG. 1 shows a FS FBMC/OQAM transmitter implementation. As shown, theimplementation of FIG. 1 comprises an OQAM mapper 110 comprising a QAMmapper 111 creating real and imaginary values from a binary input. Theimaginary values are delayed by T/2 with respect to the real values bydelay unit 112. The real and imaginary values are output to respectiveprocessing channels. Each processing channel comprises in sequence apre-processing unit 121, 122, up-sampling units 131, 132, which upscaleeach signal by a factor of q, a Finite Impulse Response (FIR) filter141, 142 and an Inverse Fast Fourier Transform block 151, 152. Theoutputs of the two processing channels are then combined by a summer160.

The original intention in this technology was to shift the filteringstage into the frequency domain, to enable the use of a low-complexityper-sub-carrier equalizer as in OFDM. The hardware complexity ispresumed to be higher than the complexity of the alternative PolyphaseNetwork (PPN) implementation, at least for long filters. In fact, itrequires one FFT of size L=qM per OQAM symbol, where q is theoverlapping factor, and M the total number of available sub-carriers.However, in a short filter case (q=1), the size of the FFT is the sameas for the PPN implementation.

FIG. 2 shows an FS FBMC/OQAM Receiver implementation. It is assumed thatthe received signal is sampled by a corresponding sampling frequency(whose value depends on the bandwidth). As shown in the figure, a firstsliding window 261 is applied on a number of samples. The number ofsamples depends on the window length.

The received signal is furthermore subjected to an M/2 delay by delayunit 270, where M is the length of the first sliding window 261 and alsoa second sliding window 262 to which the output of the delay unit 270 isfed, so that the two sliding windows 261, 262 overlap by half theirrespective lengths in number of samples. Each sliding window 261, 262outputs samples to respective Fast Fourier Transform units 251, 252.Fast Fourier Transform units 251, 252 provide their outputs torespective Digital Filters 241, 242, the outputs of which are thendown-sampled at down-sampling units 231, 232 which down-sample by afactor of q.

Typical FBMC/OQAM architectures use a prototype filter with a duration 4times longer than an OFDM symbol. However, a shorter filter can also beapplied, such as the “Quadrature Mirror Filter with OF equal to 1” whichwhen applied to FBMC/OQAM, leads to a variant denoted “Lapped-OFDMmodulation”.

When compared to long filters, short filters provide certain advantages:

-   -   Transition between two successive radio frames due to the filter        convolution is shortened, increasing the spectral efficiency of        the transmission. The overhead is only M/2 samples for a short        filter with an OF of 1, compared to 7M/2 for typical long        filters.    -   By consequence, latency is greatly reduced, and is also a        critical performance indicator for 5G. Some applications, like        vehicle to vehicle communication, have a target latency of less        than 1 millisecond.    -   Short filters are more resilient to Carrier Frequency Offset        introduced by Doppler shift and spread, or misalignment of the        local oscillator between the transmitter(s) and the receiver        which results in CFO impairment. In 5G, the transceiver has to        support mobility up to 500 km/h, 200 km/h higher than in 4G/LTE.        Furthermore, airplane connectivity is also considered in 5G,        which raises the demand to 1000 km/h. Thus, the sensitivity to        Doppler shift and CFO is a critical issue and OFDM using 4G/LTE        parameters cannot easily support such mobility requirements.    -   The hardware complexity is highly reduced when using a short        filter, particularly in terms of memory requirements. At the        transmitter side, an optimization of the FBMC/OQAM modulator is        possible and provides a hardware complexity comparable to OFDM.    -   Preamble based channel estimation using the Interference        Approximation Method (IAM) provides the best results when using        a short filter, andoutperforms OFDM. It presents however a high        Peak-to-Average Power Ratio (PAPR) making it more difficult to        use in practice.    -   Space-Time Block Coding (STBC) Multiple Input Multiple Output        (MIMO) diversity scheme can be applied with minimal spectral        efficiency loss when using the block-type implementation, due to        a shorter block transition.    -   PAPR reduction techniques are more efficient when using short        filters.

It is accordingly desirable to find short prototype filter designs withgood performance and low hardware complexity, and methodologies fordeveloping such designs. In particular, it is desirable to reduce thenumber of non-zero coefficients of the frequency response of theprototype filter for a target Signal-to-Interference-Ratio (SIR), inorder, for example, to reduce the hardware complexity of the FSimplementations of filter-bank receivers such as those implementingFBMC/OQAM.

SUMMARY OF THE INVENTION

In accordance with the present invention in a first aspect there isprovided a Filter Bank Multicarrier frequency spread receiver fordecoding a signal, where the receiver comprises a linear phase rotationmodule adapted to introduce a linear phase rotation to a time domainsignal, a discrete Fourier transform unit and a Finite Impulse Responsedigital filter, wherein the coefficients of the Finite Impulse Responsedigital filter define a shift of a frequency response of the prototypefilter of the receiver, and wherein the introduced linear phase rotationis compensated by the frequency shift of the Finite Impulse Responsedigital filter. A receiver adopting this structure can be expected tooffer improved performance in terms of Signal to Interference ratio witha reduced number of filter coefficients compared to equivalent designs.

In a development of the first aspect, the coefficients of the digitalfilter are truncated to include a minimal number of coefficientssufficient to achieve a desired Signal to Interference ratio.

In a development of the first aspect, the frequency shift is equal tothe reciprocal of a power of two of the modulation sub carrier spacing.

In a development of the first aspect, the frequency shift is equal tohalf the modulation sub carrier spacing.

In a development of the first aspect, the digital filter has fewercoefficients than the frequency response of the prototype filter.

In a development of the first aspect, the filter-bank impulse responseof the prototype filter satisfies the Nyquist criterion.

In a development of the first aspect, the prototype filter is one of theQMF filter, the TFL1 filter, or the IOTA filter.

In a development of the first aspect, the Filter Bank Multicarrierreceiver comprises a linear phase rotation module, a discrete Fouriertransform and a Finite Impulse response digital filter in a first group,and a further linear phase rotation module, a further discrete Fouriertransform and a further Finite Impulse response digital filter in asecond group, wherein the first group and second group are arranged toprocess a first signal stream and a second signal stream respectively inparallel, wherein the first signal stream and the second signal streamare orthogonal to each other.

In a further development of the first aspect, the first signal streamand the second signal stream constitute an OFDM signal.

In a further development of the first aspect, the first signal streamand the second signal stream constitute an FBMC signal.

In accordance with the present invention in a second aspect there isprovided a method of defining a filter for a digital radio receiver,comprising the steps of

-   -   defining a prototype filter,    -   obtaining a frequency shifted version of the prototype filter,        and    -   truncating the coefficients defining the frequency shifted        version of the prototype filter to the minimum number of        coefficients enabling the frequency shifted version of the        prototype filter to achieve a predefined Signal to Noise level.

In accordance with the present invention in a third aspect there isprovided method of decoding a Filter Bank Multicarrier encoded signal,comprising the steps of

-   -   obtaining digital samples s(k) at a specified sampling rate,    -   grouping the samples into groups of predetermined size,    -   imposing a frequency shift equal to a predetermined fraction of        the sub-carrier space on the groups,    -   transforming the time-domain frequency shifted and grouped        samples to the frequency domain, and then    -   filtering so as to compensate the frequency shift.

Decoding a signal on the basis of these steps can be expected to offerimproved performance in terms of Signal to Interference ratio with areduced number of filter coefficients compared to equivalent designs.

In accordance with the present invention in a fourth aspect there isprovided computer program adapted to implement the steps of the secondor third aspects.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other advantages of the present invention will now bedescribed with reference to the accompanying drawings, in which:

FIG. 1 shows a PPN FBMC/OQAM transmitter implementation;

FIG. 2 shows a FS FBMC/OQAM transmitter implementation;

FIG. 3 shows details of a first embodiment;

FIG. 4 shows the steps of a method of designing a filter in accordancewith an embodiment;

FIG. 5a illustrates the Nyquist criterion for a filter bank system;

FIG. 5b further illustrates the Nyquist criterion for a filter banksystem;

FIG. 6 shows a possible relationship between the number of coefficientsin a filter design and the specified signal to interference ratioattained;

FIG. 7 presents a receiver in accordance with an embodiment;

FIG. 8 shows a method of decoding a Filter Bank Multicarrier encodeddigital radio signal in accordance with an embodiment;

FIG. 9 shows a generic computing system suitable for implementation ofembodiments of the invention;

FIG. 10 shows a smartphone device adaptable to constitute an embodiment;and

FIG. 11 shows a cellular network base station adaptable to constitute anembodiment.

DETAILED DESCRIPTION

Multicarrier encoding schemes in general and FBMC based systems inparticular are known to be sensitive to variations in carrier frequency,known as Carrier Frequency Offset (CFO), which tend to undermine theorthogonality of adjacent sub-carriers, leading generally tointercarrier interference (ICI), and reducing performance. It is thus ageneral objective in the field of FBMC system development to minimizeCFO.

Short prototype filters for FBMC modulation have multiple advantages(low complexity, robustness to Doppler shift/CFO, latency . . . ).Combined with the Frequency-Spread (FS) implementation, the FBMCreceiver can support multipath channels with moderate delay spread(EPA/EVA LTE channels) when using a low-complexity 1 tap equalizer. ThisFS implementation shifts the time domain filtering stage (the polyphasenetwork with the impulse response of the prototype filter) to thefrequency domain (after the DFT) by using a FIR filter between theoutput of the DFT and the frequency response of the prototype filter.Using this technique, it is also possible to compensate thecarrier-frequency offset (CFO) in the frequency domain. This is done bygenerating the shifted frequency domain response of the prototype filterand using the corresponding coefficients for the FIR filter of the FSimplementation.

The inventors of the present application have determined thatunexpectedly, for some prototype filters, fewer non-zero coefficientsare required to achieve a target Signal to Interference Ratio (SIR) witha CFO compensation than with no CFO compensation.

Accordingly, it is proposed to deliberately introduce a frequencyoffset, equivalent to a linear phase rotation, in the received timedomain signals at the receiver side, and then compensate this offset inthe frequency domain by shifting the frequency response of the prototypefilter 241, 242, and thereby reduce the number of non-zero coefficientsof the FIR filter for a specified SIR.

FIG. 3 shows details of a first embodiment.

As shown in FIG. 3, there is provided a Filter Bank Multicarrierfrequency spread receiver 300 for decoding a signal from a correspondingFilter Bank Multicarrier transmitter (not shown). The receiver 300comprises a linear phase rotation module 380 adapted to introduce alinear phase rotation to a time domain signal, a discrete Fouriertransform 350, and a Finite Impulse Response digital filter 340. Thecoefficients of the digital filter 340 define a shift of the frequencyresponse of the prototype filter of the receiver, and the introducedlinear phase rotation is compensated by this frequency shift of thedigital filter.

The frequency shift implemented by the linear phase rotation module 380and compensated by the digital filter 340 is equal to the reciprocal ofa power of two of the modulation sub carrier spacing. For example, thefrequency shift implemented by the linear phase rotation module 380 andcompensated by the digital filter 340 may be ½ of the modulation subcarrier spacing, ¼ of the modulation sub carrier spacing, ⅛ of themodulation sub carrier spacing, and so on.

FIG. 4 shows the steps of a method of designing a filter in accordancewith an embodiment.

As shown in FIG. 4, the method starts at step 400 before proceeding tostep 410 at which a prototype filter g is defined.

g is a prototype of length L=qM, where q represents the overlappingfactor of the filter bank system and M the (I)DFT size of the criticallysampled polyphase decomposition of the filter-bank system. The onlyconstraint imposed by this filter is having a length which is a multipleof M, with

M∈

1,+∞

q∈

1,+∞

In many implementations M may be a power of two, and q≧4, which may tendto minimize hardware complexity and latency issues.

g can be designed from scratch using a variety of methods.

In one filter design method, the prototype filter g may be designed byoptimizing filter coefficients in the frequency domain to fulfilTime-Frequency Localization requirements and the Nyquist Criterion.

FIG. 5a illustrates the Nyquist criterion for a filter bank system. Asshown in FIG. 5a , a prototype filter impulse response 500 is plottedwith time on the x axis 501 and power on the y axis 502. A first filterresponse 503 is plotted at a first time 505, and a second filterresponse 504 is plotted at a second time 506, the two time-shiftedfilter responses being separated by a time shift b, 507.

FIG. 5b further illustrates the Nyquist criterion for a filter banksystem. As shown in FIG. 5b , the prototype filter impulse response 500of FIG. 5a is plotted, with time on the x axis 501 and power on the yaxis 502. A first filter response 508 is plotted at a third time 510,and a fourth filter response 509 is plotted at a second time 511, thetwo time-shifted filter responses being separated by the same time shiftb as for FIG. 5a , 507.

Although in FIGS. 5a and 5b the abscissa for the filter responses isdifferent (a and g respectively), the total of the powers of the firstand second filter responses c+d is equal to the total of the powers ofthe third and four filter responses e+f. For a prototype filter of afilter bank satisfying the Nyquist criterion, this will be true for anypair of filter responses shifted by the same time.

Accordingly, the filter-bank impulse response of the prototype filtermay be selected as satisfying the Nyquist criterion.

Another design method involves the optimization of filter coefficientsusing a compact representation by decomposing the impulse response ofthe filter into an angular-based representation of the correspondingpolyphase network. This representation ensures that the Nyquistcriterion is respected, and the angular parameters are optimized to meetthe TFL criterion. This method is described in D. Pinchon, P. Siohan,and C. Siclet, “Design techniques for orthogonal Modulated filterbanksbased on a compact representation,” IEEE Transactions on SignalProcessing, vol. 52, no. 6, pp. 1682-1692, June 2004.

Other design methods involve the Isotropic Orthogonal TransformAlgorithm (IOTA) as described by B. le Floch, M. Alard, C. Berrou. in“Coded orthogonal frequency division multiplex”. Proceedings of theIEEE, vol. 83, pp. 982-996, June 1995, or the Square Root Raised Cosinefunctions.

Filters developed according to the above principles are particularlysuited for digital modulation schemes such as cyclic or linearconvolution based communication systems, for example.

Still further, prototype filter designs selected from known prototypefilter designs may also be found to satisfy selection criteria asdiscussed above, and provide the basis of new filter designs for this orother applications, such as

-   -   IOTA Filter as described in B. Le Floch, M. Alard, and C.        Berrou, “Coded orthogonal frequency division multiplex [TV        broadcasting],” Proceedings of the IEEE, vol. 83, no. 6, pp.        982-996, June 1995    -   FS 4 filter as described in D. Pinchon, P. Siohan, C. Siclet,        Design techniques for orthogonal modulated filter banks based on        a compact representation, IEEE Trans. Signal Process. 52 (June        (6)) (2004) 1682-1692.    -   MMB filter with OF superior to 4 as described in K. Martin,        “Small side-lobe filter design for multitone data-communication        applications,” IEEE Transactions on Circuits and Systems II:        Analog and Digital Signal Processing, vol. 45, no. 8, pp.        1155-1161, August 1998.    -   QMF filter. as described in “Modulated QMF filter banks with        perfect reconstruction,” by H. Malvar, Electronics Letters, vol.        26, no. 13, pp. 906-907, June 1990.    -   TFL1 filter as described by D. Pinchon and P. Siohan, in        “Derivation of analytical expressions for flexible PR low        complexity FBMC systems,” in Signal Processing Conference        (EUSIPCO), 2013 Proceedings of the 21st European, September        2013.

By way of example a half sine filter may be adopted as the prototypefilter, whereby for q=1

$\begin{matrix}{{{g(k)} = {\sin \left( \frac{\pi \; k}{M} \right)}},{k \in {〚{0,{M - 1}}〛}}} & (9)\end{matrix}$

On this basis, the following coefficients may be obtained by applying adiscrete Fourier transform of size M=512:

G(0)=0.6366

G(1)=−0.2122

G(2)=−0.0424

G(3)=−0.0182

G(4)=−0.0101

G(5)=−0.0064

G(6)=−0.0045

G(7)=−0.0033

G(8)=−0.0025

G(9)=−0.0020

Once the prototype filter is defined at step 410, the method proceeds tostep 420, at which a frequency shifted prototype filter G_(HFS) isobtained. If the frequency is shifted by half of the sub-carrier spacingfor example, the following calculation applies:

$\begin{matrix}{{G_{HFS}(m)} = {\frac{1}{qM}{\sum\limits_{k = 0}^{{qM} - 1}{{g(k)}e^{{- i}\; 2{\pi ɛ}\frac{k}{M}}e^{{- i}\; 2\pi \; k\frac{m}{qM}}}}}} & (10)\end{matrix}$

Where ε=½ or ε=−½. Both definitions are possible, and lead to the sameperformance.

This equation may be computed using the following algorithm:

Step A: Multiply g(k) by

$e^{{- i}\; 2{\pi ɛ}\frac{k}{M}},$

k∈[0, qM−1], to obtain g_(HFS)(k)

Step B: Compute the Discrete Fourier Transform of size qM of g_(HFS)(k)to obtain G_(HFS)(m).

The method may then terminate. Optionally, the method may comprise anadditional step 430, whereby the coefficients of the frequency shiftedfilter may be truncated, so as to strike the desired compromise betweenimplementation complexity in terms of the number of taps in the circularconvolution, and performance in terms of Signal to Interference Ratio.

The truncation of the frequency shifted filter may be obtained byretaining a selected number C_(g) of non-zero coefficients.

FIG. 6 shows a possible relationship between the number of coefficientsin a filter design and the specified signal to interference ratioattained. As shown, the Signal to Interference performance correspondingto certain prototype filters mentioned above is plotted against thenumber of coefficients retained after truncation. Specifically, line 610represents the Signal to Interference performance for the TFL1 filterwithout frequency shift and line 611 represents the Signal toInterference performance for the TFL1 filter with frequency shift. Ascan be seen, the performance of the frequency shifted filters isgenerally superior to that of the un-shifted version. It is furtherclear that the performance improvement for additional coefficientsrapidly tails off for most filter designs.

As such, the coefficients of the digital filter may be truncated toinclude the minimal number of coefficients sufficient to achieve adesired Signal to Interference ratio.

The digital filter may thus have fewer coefficients than the frequencyresponse of the prototype filter.

Applying this to the half sine filter example, with a value of ε=−½, thefollowing Frequency Shifted values are obtained:

G_(HFS)(0) = 0.5i G_(HFS)(1) = −0.5i G_(HFS)(2) = 0 G_(HFS)(3) = 0(…) G_(HFS)(9) = 0

Thus in this example only two coefficients need be retained, and theothers may be truncated without degradation in performance.

The method then terminates at step 440.

FIG. 7 presents a receiver in accordance with an embodiment.

Specifically, FIG. 7 shows an FS FBMC/OQAM Receiver similar to that ofFIG. 2, incorporating the elements described with reference to FIG. 3.As shown, a received signal is sampled by a first sliding window 261.The received signal is furthermore subjected to a M/2 delay by delayunit 270, where M is the length of the first sliding window 261 and alsoa second sliding window 262 to which the output of the delay unit 270 isfed, so that the sampled periods of the two sliding windows 261, 262overlap by half their respective lengths. Each sliding window 261, 262outputs samples to respective phase rotation modules 781, 782, eachcorresponding to the linear phase rotation module 380 described abovewith reference to FIG. 3. Phase rotation modules 781, 782 provide theiroutputs to Fast Fourier Transform units 251, 252. Fast Fourier Transformunits 251, 252 provide their outputs to respective Digital Filters 741,742, which are configured to implement the filter function G_(HFS)discussed above, the outputs of which are then down-sampled atdown-sampling units 231, 232 which down-sample by a factor of q.

More specifically, digital samples s(k) obtained after the analogue todigital converter (not shown) at the frequency sampling rate of thesystem are grouped into N groups of qM samples. N is dependent on thesystem parameters of the modulation used, and may be for example thenumber of multicarrier symbols.

s _(n)(k)=s(k+I _(n)),k∈

0,qM−1

,n∈

0,N−1

where I_(n) represents the first index of interval which defines thegroup number n, and s_(n) the samples if the group number n. Forinstance, in an FBMC/0QAM system such as shown in figure

${{7I_{n}} = {n\frac{M}{2}}},$

whereas for OFDM I_(n)=nM (and q=1).

In accordance with the present embodiment the frequency shiftimplemented by phase rotation modules 781, 782 is equal to half thesub-carrier sp ace.

On this basis, the N group baseband samples s_(n) are computed as

${v_{n}(k)} = {{s_{n}(k)}e^{i\; 2{\pi ɛ}\frac{k}{M}}}$

Where ε=½ or ε=−½ depending on the choice made during the design of thefilter as described above.

The DFTs 251, 252 next transform the time-domain frequency shifted andgrouped base-band samples output by the phase rotation modules 681, 682to the frequency domain. With DFTs of size qM,

$\begin{matrix}{{x_{n}(m)} = {\sum\limits_{k = 0}^{{qM} - 1}{{v_{n}(k)}e^{{- i}\; 2\pi \frac{km}{qM}}}}} & (11)\end{matrix}$

Finally, the effect of the FIRs C_(G) can be efficiently calculated byapplying a circular convolution:

$\begin{matrix}{{y_{n}(m)} = {\sum\limits_{k \in \Omega}{{G_{HFS}(k)}{x_{n}\left( {{mod}_{qM}\left( {m - k} \right)} \right)}}}} & (12)\end{matrix}$

Where mod_(qm) represents the modulus qM operator, and Ω is the valueobtained from the number of coefficients retained at truncation of thefilter as described above, in accordance with the following:

If C_(g) is an even number, Ω=

−Δ+1, Δ

or Ω=

−Δ, Δ+1

, where Δ=C_(g)/2

If C_(g) is an odd number, Ω=

−Δ, Δ

, where Δ=(C_(G)−1)/2

While FIG. 7 presents an OQAM receiver, and as such provides twoindependent channels for the processing of I and Q symbols respectively,each corresponding to the components of FIG. 3, other implementationsare envisaged, for example implementing any filter-bank based modulationscheme, whether orthogonal or not, OQAM or not. If OQAM is not used,only one component is applied, for instance in the case of FBMC/QAM, FMTand the like.

The implementation of the filter depends on the encoding schemearchitecture, and may use any conventional filter architecture as willbe apparent to the skilled person.

FIG. 8 shows a method of decoding a Filter Bank Multicarrier encodeddigital radio signal in accordance with an embodiment.

Digital samples s(k) are obtained at step 810 at the frequency samplingrate of the system, and grouped into P groups of qM samples at step 820,corresponding to the sliding window operation. P is dependent on thesystem parameters of the modulation used, and may be for example thenumber of multicarrier symbols.

s _(n)(k)=s(k+I _(n)),k∈

0,qM−1

,n∈

0,P−1

where I_(n) represents the first index of interval which defines thegroup number n, and s_(n) the samples if the group number n. Forinstance, in an

FBMC/OQAM system such as shown in FIG. 7,

${I_{n} = {n\frac{M}{2}}},$

whereas for OFDM In=nM (and q=1).

The method next proceeds to step 830 at which a frequency shift isimposed on the signal.

If the frequency shift is equal to half the sub-carrier space, the Ngroup baseband samples s_(n) are computed as

${v_{n}(k)} = {{s_{n}(k)}e^{i\; 2{\pi ɛ}\frac{k}{M}}}$

Where ε=½ or ε=−½ depending on the choice made during the design of thefilter as described above with reference to FIG. 4.

The method next proceeds to step 840, at which the time-domain frequencyshifted and grouped base band samples are derived at step 430 aretransformed to the frequency domain. For example, with DFTs of size qM,

$\begin{matrix}{{X_{n}(m)} = {\sum\limits_{k = 0}^{{qM} - 1}{{v_{n}(k)}e^{{- 2}\pi \frac{km}{qM}}}}} & (13)\end{matrix}$

Finally, at step 850 the filter effect C_(G) compensating the frequencyshift as determined in accordance for example with the method of FIG. 4can be applied, for example by applying a circular convolution:

$\begin{matrix}{{y_{n}(m)} = {\sum\limits_{k \in \Omega}{{G_{HFS}(k)}{x_{n}\left( {{mod}_{qM}\left( {m - k} \right)} \right)}}}} & (14)\end{matrix}$

Where mod_(qm) represents the modulus qM operator, and Ω is a valueobtained from the number of coefficients retained at truncation of thefilter as described above, in accordance with the following: If C_(g) isan even number, ≠=

−Δ+1, Δ

or Ω=

−Δ, Δ+1

, where Δ=C_(g)/2 If C_(g) is an odd number, Ω=

−Δ, Δ

, where Δ=(C_(g-1))/2

The method then proceeds to step 860, at which the filtered values aredown-sampled by a factor q, such that

c _(n)(m)=y _(n)(qm),

With c_(n)(m) being the output sample of the synthesis filter at thesub-carrier number m, time slot n

The down-sampled values produced by this operation thus correspond tothe output of the synthesis filter (filter-bank receiver).

The resulting values can then be decoded by means of an OQAM demapper inthe conventional manner (not shown).

The method then terminates at step 870.

For a PPN-based implementation, the filter is used as a window function,thus it is simply a multiplication of the coefficients at the input ofthe FFT (receiver side). For this implementation, it is preferable touse the non-truncated version. This implies no change in complexity.

For a Frequency Spread-based implementation, the filter is implementedas a discrete-time FIR filter, after the FFT on the receiver side. Thetruncated version may be used to reduce the complexity.

In some cases a PPN implementation at the transmitter side and FrequencySpread implementation at Receiver side may prove advantageous. Otherimplementation details and variants of these methods may be envisaged,in particular corresponding to the variants of the apparatus describedwith reference to the preceding drawings.

Thus according to certain embodiments there is provided a receiver forFilter Bank Multicarrier frequency spread signals such as FBMC,FBMC/OQAM, OFDM, comprising a linear phase rotation module adapted tointroduce a linear phase rotation to a received time domain signal, adiscrete Fourier transform and a Finite Impulse response digital filter.The coefficients of the digital filter define a shift of the frequencyresponse of the prototype filter of the receiver, and the coefficientsof the digital filter are fixed so as to compensate the linear phaserotation introduced by the filter. The frequency shift introduced may beequal to the reciprocal of a power of two of the modulation sub carrierspacing.

The disclosed methods can take form of an entirely hardware embodiment(e.g. FPGA), an entirely software embodiment (for example to control asystem according to the invention) or an embodiment containing bothhardware and software elements. Software embodiments include but are notlimited to firmware, resident software, microcode, etc. The inventioncan take the form of a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or an instruction executionsystem. A computer-usable or computer-readable can be any apparatus thatcan contain, store, communicate, propagate, or transport the program foruse by or in connection with the instruction execution system,apparatus, or device. The medium can be an electronic, magnetic,optical, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium.

These methods and processes may be implemented by means ofcomputer-application programs or services, an application-programminginterface (API), a library, and/or other computer-program product, orany combination of such entities.

FIG. 9 shows a generic computing system suitable for implementation ofembodiments of the invention.

A shown in FIG. 9, a system includes a logic device 901 and a storagedevice 902. The system may optionally include a display subsystem 911,input/output subsystem 903, communication subsystem 920, and/or othercomponents not shown.

Logic device 901 includes one or more physical devices configured toexecute instructions. For example, the logic device 901 may beconfigured to execute instructions that are part of one or moreapplications, services, programs, routines, libraries, objects,components, data structures, or other logical constructs. Suchinstructions may be implemented to perform a task, implement a datatype, transform the state of one or more components, achieve a technicaleffect, or otherwise arrive at a desired result.

The logic device 901 may include one or more processors configured toexecute software instructions. Additionally or alternatively, the logicdevice may include one or more hardware or firmware logic devicesconfigured to execute hardware or firmware instructions. Processors ofthe logic device may be single-core or multi-core, and the instructionsexecuted thereon may be configured for sequential, parallel, and/ordistributed processing. Individual components of the logic device 901optionally may be distributed among two or more separate devices, whichmay be remotely located and/or configured for coordinated processing.Aspects of the logic device 901 may be virtualized and executed byremotely accessible, networked computing devices configured in acloud-computing configuration.

Storage device 902 includes one or more physical devices configured tohold instructions executable by the logic device to implement themethods and processes described herein. When such methods and processesare implemented, the state of storage 902 device may betransformed—e.g., to hold different data.

Storage device 902 may include removable and/or built-in devices.Storage device 902 may comprise one or more types of storage deviceincluding optical memory (e.g., CD, DVD, HD-DVD, Blu-Ray Disc, etc.),semiconductor memory (e.g., FLASH, RAM, EPROM, EEPROM, etc.), and/ormagnetic memory (e.g., hard-disk drive, floppy-disk drive, tape drive,MRAM, etc.), among others. Storage device may include volatile,nonvolatile, dynamic, static, read/write, read-only, random-access,sequential-access, location-addressable, file-addressable, and/orcontent-addressable devices.

In certain arrangements, the system may comprise an i/o interface 903adapted to support communications between the Logic device 901 andfurther system components. For example, additional system components maycomprise removable and/or built-in extended storage devices. Extendedstorage devices may comprise one or more types of storage deviceincluding optical memory 932 (e.g., CD, DVD, HD-DVD, Blu-Ray Disc,etc.), semiconductor memory 933 (e.g., FLASH RAM, EPROM, EEPROM, FLASHetc.), and/or magnetic memory 931 (e.g., hard-disk drive, floppy-diskdrive, tape drive, MRAM, etc.), among others. Such extended storagedevice may include volatile, nonvolatile, dynamic, static, read/write,read-only, random-access, sequential-access, location-addressable,file-addressable, and/or content-addressable devices.

It will be appreciated that storage device includes one or more physicaldevices, and excludes propagating signals per se. However, aspects ofthe instructions described herein alternatively may be propagated by acommunication medium (e.g., an electromagnetic signal, an opticalsignal, etc.), as opposed to being stored on a storage device.

Aspects of logic device 901 and storage device 902 may be integratedtogether into one or more hardware-logic components. Such hardware-logiccomponents may include field-programmable gate arrays (FPGAs), program-and application-specific integrated circuits (PASIC/ASICs), program- andapplication-specific standard products (PSSP/ASSPs), system-on-a-chip(SOC), and complex programmable logic devices (CPLDs), for example.

The term “program” may be used to describe an aspect of computing systemimplemented to perform a particular function. In some cases, a programmay be instantiated via logic device executing machine-readableinstructions held by storage device. It will be understood thatdifferent modules may be instantiated from the same application,service, code block, object, library, routine, API, function, etc.Likewise, the same program may be instantiated by differentapplications, services, code blocks, objects, routines, APIs, functions,etc. The term “program” may encompass individual or groups of executablefiles, data files, libraries, drivers, scripts, database records, etc.

In particular, the system of FIG. 9 may be used to implement embodimentsof the invention.

For example a program implementing the steps described with respect toFIG. 4 or 8 may be stored in storage device 902 and executed by logicdevice 901. The prototype filter design may be buffered in the storagedevice 902. The Logic device 901 may implement the Phase rotation,Fourier Transform or Filter steps as described above under the controlof a suitable program, or may interface with internal or externaldedicated systems adapted to perform some or all of these processes suchas hardware accelerated encoders/decoders and the like. Furthermore, aprogram may implement a transmitter or receiver implementing an encoderor decoder in accordance with embodiments for example as describedabove. These tasks may be shared among a number of computing devices,for example as described with reference to FIG. 9. The encoded signalmay be received via the communications interface 920, which mayincorporate implementations of some or all of the elements of FIG. 7.

Accordingly the invention may be embodied in the form of a computerprogram.

It will be appreciated that a “service”, as used herein, is anapplication program executable across multiple user sessions. A servicemay be available to one or more system components, programs, and/orother services. In some implementations, a service may run on one ormore server-computing devices.

When included, display subsystem 911 may be used to present a visualrepresentation of the data transmitted or received, or may presentstatistical information concerning the processes undertaken. As theherein described methods and processes change the data held by thestorage device 902, and thus transform the state of the storage device902, the state of display subsystem 911 may likewise be transformed tovisually represent changes in the underlying data. Display subsystem 911may include one or more display devices utilizing virtually any type oftechnology. Such display devices may be combined with logic deviceand/or storage device in a shared enclosure, or such display devices maybe peripheral display devices.

When included, input subsystem may comprise or interface with one ormore user-input devices such as a keyboard 912, mouse 913, touch screen911, or game controller (not shown). In some embodiments, the inputsubsystem may comprise or interface with selected natural user input(NUI) componentry. Such componentry may be integrated or peripheral, andthe transduction and/or processing of input actions may be handled on-or off-board. Example NUI componentry may include a microphone forspeech and/or voice recognition; an infrared, colour, stereoscopic,and/or depth camera for machine vision and/or gesture recognition; ahead tracker, eye tracker, accelerometer, and/or gyroscope for motiondetection and/or intent recognition; as well as electric-field sensingcomponentry for assessing brain activity.

When included, communication subsystem 920 may be configured tocommunicatively couple computing system with one or more other computingdevices. For example, communication module of may communicatively couplecomputing device to remote service hosted for example on a remote server976 via a network of any size including for example a personal areanetwork, local area network, wide area network, or the internet.Communication subsystem may include wired and/or wireless communicationdevices compatible with one or more different communication protocols.As non-limiting examples, the communication subsystem may be configuredfor communication via a wireless telephone network 974, or a wired orwireless local- or wide-area network. In some embodiments, thecommunication subsystem may allow computing system to send and/orreceive messages to and/or from other devices via a network such as theInternet 975. The communications subsystem may additionally supportshort range inductive communications 921 with passive devices (NFC, RFIDetc).

FIG. 10 shows a smartphone device adaptable to constitute an embodiment.As shown in FIG. 10, the smartphone device incorporates elements 901,902, 903, 920, near field communications interface 921, flash memory933, elements 914, 915, and 911 as described above. It is incommunication with the telephone network 974 and a server 976 via thenetwork 975. Although shown as a smartphone, equivalent functionalitymay be implemented in any radio communications device, such as afeature-phone, tablet device and so forth.

FIG. 11 shows a cellular network base station adaptable to constitute anembodiment. As shown in FIG. 11, the cellular network base stationincorporates elements 901, 902, 903, 920, as described above. It is incommunication with the telephone network 974 and a server 976 via thenetwork 975.

It will be understood that the configurations and/or approachesdescribed herein are exemplary in nature, and that these specificembodiments or examples are not to be considered in a limiting sense,because numerous variations are possible. The specific routines ormethods described herein may represent one or more of any number ofprocessing strategies. As such, various acts illustrated and/ordescribed may be performed in the sequence illustrated and/or described,in other sequences, in parallel, or omitted. Likewise, the order of theabove-described processes may be changed.

The subject matter of the present disclosure includes all novel andnon-obvious combinations and sub-combinations of the various processes,systems and configurations, and other features, functions, acts, and/orproperties disclosed herein, as well as any and all equivalents thereof.

1. A Filter Bank Multicarrier frequency spread receiver for decoding a signal, said receiver comprising a linear phase rotation module adapted to introduce a linear phase rotation to a time domain signal, a Discrete Fourier Transform unit, and a Finite Impulse Response digital filter, wherein coefficients of said Finite Impulse Response digital filter define a shift of a frequency response of a prototype filter of said receiver, and wherein said introduced linear phase rotation is compensated by the frequency shift of said Finite Impulse Response digital filter.
 2. A Filter Bank Multicarrier receiver according to claim 1, wherein the coefficients of said digital filter are truncated to include a minimal number of coefficients sufficient to achieve a desired Signal to Interference ratio.
 3. A Filter Bank Multicarrier receiver according to claim 1 wherein said frequency shift is equal to the reciprocal of a power of two of the modulation sub carrier spacing.
 4. A Filter Bank Multicarrier receiver according to claim 3, wherein said frequency shift is equal to half the modulation sub carrier spacing.
 5. A Filter Bank Multicarrier receiver according to claim 1 where said digital filter has fewer coefficients than the frequency response of said prototype filter.
 6. A Filter Bank Multicarrier receiver according to claim 1, wherein the filter-bank impulse response of the prototype filter satisfies the Nyquist criterion.
 7. Filter Bank Multicarrier receiver according to claim 1, wherein said prototype filter is one of the QMF filter, the TFL1 filter, or the IOTA filter.
 8. A Filter Bank Multicarrier receiver in accordance with claim 1 comprising a linear phase rotation module, a discrete Fourier transform unit, and a Finite Impulse response digital filter in a first group, and a further linear phase rotation module, a further discrete Fourier transform unit and a further Finite Impulse response digital filter in a second group, wherein said first group and second group are configured to process a first signal stream and a second signal stream respectively in parallel, wherein said first signal stream and said second signal stream are orthogonal to each other.
 9. The Filter Bank Multicarrier receiver of claim 8 wherein said first signal stream and said second signal stream constitute an OFDM signal.
 10. The Filter Bank Multicarrier receiver of claim 8 wherein said first signal stream and said second signal stream constitute an FBMC signal.
 11. A method of defining a filter for a digital radio receiver, said method comprising defining a prototype filter, obtaining a frequency shifted version of said prototype filter, and truncating coefficients defining said frequency shifted version of said prototype filter to a minimum number of coefficients enabling said frequency shifted version of said prototype filter to achieve a predefined Signal to Noise level.
 12. A method of decoding a Filter Bank Multicarrier encoded signal, said method comprising obtaining digital samples at a specified sampling rate, grouping said samples into groups of predetermined size, imposing a frequency shift equal to a predetermined fraction of the sub-carrier space on said groups, transforming the time-domain frequency shifted and grouped samples to the frequency domain, and filtering the frequency domain shifted values to compensate said frequency shift.
 13. A computer program stored on a non-transitory medium adapted to implement the method of claim
 11. 14. A computer program stored on a non-transitory medium adapted to implement the method of claim
 12. 